ORLANDO, Fla. — The Giants thought newly signed offensive lineman John Jerry was in the clear, but that may no longer be the case.

Contradicting statements made by coach Tom Coughlin on Wednesday morning and by co-owner John Mara on Sunday, the Giants issued a clarification Wednesday afternoon saying they now understand Jerry could face suspension or other punishment stemming from his alleged involvement in the Dolphins’ bullying scandal.

Speaking at the NFC coaches breakfast during the NFL owners meetings, Coughlin told reporters the Giants had contacted the league office and been assured Jerry wouldn’t face a suspension

“There is no suspension in the air or anything of that nature,” Coughlin had said.

But Goodell, speaking after the Giants coach, said nothing has been ruled out beyond the mandatory mental-health evaluation Jerry will have to go through after being named more than 100 times in the Wells Report as a tormenter of former Dolphins lineman Jonathan Martin.

“From our standpoint, the medical evaluation will determine what happens,“ Goodell said during his news conference to close out the annual meetings.

Jerry signed a one-year, $795,000 deal with the Giants last Friday after Coughlin said general manager Jerry Reese and the team’s scouting department vouched for the veteran blocker.

Coughlin said Jerry — who allegedly started the hazing of Martin in 2012 by challenging him to a fight in the locker room — was apologetic about his alleged behavior, and the Giants boss doesn’t expect Jerry to repeat it with his new club.

“They thought he was being honest and straightforward with whatever part he played in [the bullying],” Coughlin said. “There was sincere remorse. We still feel very strongly about our locker room, the players that are there for us. I don’t see that happening with us, anything of that nature.”

Coughlin also touched on several other topics in the hour-long chat, including the free-agent defections of Justin Tuck and Hakeem Nicks, the addition of Dominique Rodgers-Cromartie and the other veteran free agents the Giants brought in and what the offense needs to look like under new coordinator Ben McAdoo.

Coughlin said the Giants wanted to keep Tuck, but couldn’t compete with the two-year, $10 million deal he ended up receiving from the Raiders.

“We’re going to miss Justin Tuck, period,” Coughlin said. “The body of work last year was very solid.”

Coughlin wasn’t as downcast about the loss of Nicks, who signed a one-year deal with the Colts after two disappointing seasons with the Giants. Nicks failed to score a touchdown last year.

“The production isn’t what it should’ve been last year,” Coughlin said. “We wish Hakeem success, nothing but the best for him. Perhaps this is what he needed, the change he needed.”

Coughlin, meanwhile, said Rodgers-Cromartie will be the Giants’ top cornerback, assigned to opponents’ best receivers. The coach appeared to be more excited, though, about the possibility of big bodies such as Jerry and veteran lineman Geoff Schwartz reviving the Giants’ moribund running game.

“Offensively we have to get back to Giants football,” Coughlin said. “When I say that, I mean Jerry and Geoff — big human beings in the NFC East. We weren’t very big up front last year. It’s further to run around those big guys. We’re going to have balance [between run and pass].”

Coughlin was most animated when asked about himself, particularly what he thought of his chances of eventually being inducted into the Pro Football Hall of Fame and how much longer he expects to coach.

“I think it merits consideration, yeah, but that’s as far as I’m going,” Coughlin said of his résumé for Canton. “I don’t think about it every day. I’d rather think about getting a group of players together that we can coach to win a game.”

Coughlin will be 68 this season, making him the oldest coach in the league, but he still wants to coach for several more years.